Can we identify Walrasian allocations?

We consider a discrete time, pure exchange infinite horizon economy with $ n\geq 2$ consumers and $\ell \geq 1$ consumption goods per period. Within the framework of decentralized mechanisms, we show that for any given consumption trade at any period of time, say at time one, the consumers will need in general an infinite dimensional (informational) space to identify such a trade as an intertemporal Walrasian one. However, we show a set of environments where the Walrasian trades at each period of time can be achieved as the equilibrium trades of a sequence of decentralized competitive mechanisms, using only both current prices and quantities to coordinate decisions.Walrasian allocation, informational decentralization, mechanism design